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Some Generalizations of \(*\)-Lie Derivable Mappings and Their Characterization on Standard Operator Algebras

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Abstract

We introduce generalizations of \( *\)-Lie derivable mappings (which are not necessarily linear) on \(*\)-algebras and then provide characterizations of these generalizations on standard operator algebras. Indeed, if \( {\mathcal {H}} \) is an infinite dimensional complex Hilbert space and \( {\mathcal {A}} \) be a unital standard operator algebra on \( {\mathcal {H}} \) which is closed under the adjoint operation, then we characterize these mappings on \({\mathcal {A}}\), especially we show that these mappings are linear. Our results are various generalizations of the main result of [W. Jing, Nonlinear \(*\)-Lie derivations of standard operator algebras, Quaestiones Math. 39 (2016), 1037–1046].

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Acknowledgements

The authors thank the referee(s) for careful reading of the manuscript and for helpful suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Kurdistan, P.O. Box 416, Sanandaj, Kurdistan, Iran

    Behrooz Fadaee, Hoger Ghahramani & Heydar Moradi

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  1. Behrooz Fadaee
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  2. Hoger Ghahramani
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  3. Heydar Moradi
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Correspondence to Hoger Ghahramani.

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Communicated by Mohammad Reza Koushesh.

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Fadaee, B., Ghahramani, H. & Moradi, H. Some Generalizations of \(*\)-Lie Derivable Mappings and Their Characterization on Standard Operator Algebras. Bull. Iran. Math. Soc. 49, 66 (2023). https://doi.org/10.1007/s41980-023-00812-5

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  • DOI: https://doi.org/10.1007/s41980-023-00812-5

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